To rotate a figure: Draw a segment connecting a vertex (we will call point A) of the figure and the center of rotation We will call Point P). Using a protractor and segment AP as one side of an angle, measure the degree of rotation in the direction indicated (clockwise or counterclockwise)and draw a ray for the other side of the angle. Use a compass or ruler to measure the length of segment AP. Then, use the compass or ruler to mark the same distance on the new ray drawn in step 2. This marking (point) will be the new image’s vertex A’ Repeat for each vertex in the figure, draw segments connecting the new images vertices.

To see an example, look on page 413 of the online text To see an example, look on page 413 of the online text. Once you click the link, you will need to: Login using username “mathbooks” and password “mathbooks” Click the “geometry” text book Type 413 in the “jump to page” window at top of the page

Lessons 13.6: Rotations Transformations: 1) Translation 2) Reflection 3) Rotation Rotation: a “turning” move - geometric figure is turned about a fixed point called the center of rotation Angle of Rotation: Formed by rays drawn from the center of rotation to a point on the figure and to the corresponding point on the new image. Isometry: A transformation that preserves (keeps the same) lengths *** Rotations, reflections, and translations are isometric

Example of Rotation – Rotate 90 clockwise about the origin   A B’ A’ B C C’ A’ (6, 5) B’ (1, 5) C’ (1, 2)

Example of Rotation – Rotate 90 counterclockwise about the origin   A B C A’ (-6, -5) B’ (-1, -5) C’ (-1, -2 C’ A’ B’

Example of Rotation – Rotate 180 clockwise about the origin   A B C B’ A’ (5, -6) B’ (5, -1) C’ (2, -1 C’ A’

Example of Rotation – Rotate 180 counterclockwise about the origin   A B C B’ A’ 5, -6) B’ (5, -1) C’ (2, -1 C’ A’

Rotating about the origin Rotate 90 Clockwise Rotate 90 Counterclockwise: Rotate 180 Clockwise or Counterclockwise: Switch x and y coordinates, multiply new y-coord. by -1 (x, y)  (y, -x) Switch x and y coordinates, multiply new x-coord. by -1 (x, y)  (-y, x) Multiply both x and y by -1 (NO switching of coordinates) (x, y)  (-x, -y)

Does the following figure have rotational symmetry? A figure has Rotational Symmetry if a rotation of 180 or less clockwise (or counterclockwise) about its center produces an image that fits exactly on the original figure. (turn paper to see if rotational symmetry) Example : Does the following figure have rotational symmetry?                                                                                   Rotate 90° counterclockwise Rotate 90° Rotate 180° Has rotational symmetry for rotating clockwise or counterclockwise 90° or 180° .

Examples: State whether the figure does or does not have rotational symmetry 1) 2) 3) 4) NO YES NO YES